539.36 Modeling microstructural model of the plasticity deformation theory for quasi-isotropic composite materials
Dimitrienko Y. I. (Bauman Moscow State Technical University), Sborschikov S. V. (Bauman Moscow State Technical University), Dimitrienko A. Y. (Lomonosov Moscow State University), Yurin Y. V. (Bauman Moscow State Technical University)
COMPOSITES, NUMERICAL SIMULATION, DEFORMATION THEORY OF PLASTICITY, QUASI-ISOTROPIC MATERIALS, MICROSTRUCTURAL MODEL, ASYMPTOTIC AVERAGING METHOD, FINITE ELEMENT METHOD, DISPERSED-REINFORCED COMPOSITES, METAL COMPOSITES, DEFORMATION DIAGRAMS, INVARIANTS
doi: 10.18698/2309-3684-2021-4-1744
A model of constitutive relations for elastic-plastic composites with cubic symmetry of properties is proposed. This class includes a significant number of composite materials: dispersed-reinforced composites, which have an ordered rather than a chaotic reinforcement system, as well as some types of spatially reinforced composites. To build a model of nonlinear constitutive relations, a tensor-symmetry approach was used, based on the spectral expansions of stress and strain tensors, as well as the spectral representation of nonlinear tensor relations between these tensors. The deformation theory of plasticity is considered, for which the tensor-symmetric approach is used, and specific models are proposed for plasticity functions that depend on the spectral invariants of the strain tensor. To determine the model constants, a method is proposed in which these constants are calculated based on the approximation of deformation curves obtained by direct numerical solution of three-dimensional problems on the periodicity cell of elastic-plastic composites. These problems arise in the method of asymptotic averaging of periodic media. To solve problems on a periodicity cell, a finite element method and special software was used that implements solutions to problems on periodicity cells, developed at the Scientific and Educational Center for Supercomputer Engineering Modeling and Development of Software Packages of Bauman Moscow State Technical University. An example of calculating the constants of a composite model using the proposed method for a dispersed-reinforced composite based on a metal matrix is considered. Also, the verification of the proposed model for various ways of multiaxial loading of the composite was carried out with direct numerical simulation. It is shown that the proposed microstructural model and the algorithm for determining its constants provide a sufficiently high accuracy in predicting the elastic-plastic deformation of the composite.
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Certificate no. 2019666176 Programma NonlinearEl_Disp_Manipula dlya prognozirovaniya diagramm nelinejno-uprugogo deformirovaniya dispersno-armirovannyh kompozitov pri malyh deformaciyah na osnove konechno-elementnogo resheniya 3D lokal'nyh zadach mikromekhaniki: svidetel'stvo ob ofic. registracii programmy dlya EVM [The program NonlinearEl_Disp_Manipula for predicting diagrams of nonlinear elastic deformation of dispersed-reinforced composites under small deformations based on the finite element solution of 3D local problems of micromechanics: certificate of ofic. registration of a computer program] / Yu.I. Dimitrienko, Yu.V. Yurin, S.V. Sobshchikov, I.O. Bogdanov; applicant and copyright holder: BMSTU — no. 2019665098; application 26.11.2019; registered in the register of computer programs 05.12.2019 — [1].
Certificate no. 2019666172 Programma StrengthCom SMCM dlya konechno-elementnogo rascheta prochnostnyh harakteristik kompozitnyh materialov so slozhnoj strukturoj s uchetom nakopleniya mikro-povrezhdenij i kinetiki mezoskopicheskih defektov: svidetel'stvo ob ofic. registracii program-my dlya EVM [The StrengthCom SMCM program for finite element calculation of strength characteristics of composite materials with a complex structure, taking into account the accumulation of micro-damage and the kinetics of mesoscopic defects]: certificate of ofic. registration of a computer program / Yu. I. Dimitrienko, E. A. Gubareva, Yu. V. Yurin, S. V. Sobshchikov, I. O. Bogdanov; applicant and copyright holder: BMSTU — no. 2019665109; application 26.11.2019; registered in the register of computer programs 05.12.2019 — [1].
Certificate no. 2018614767 Programma MultiScale_SMCM dlya mnogomasshtabnogo modelirovaniya napryazhenno-deformirovannogo sostoyaniya konstrukcij iz kompozicionnyh materialov, na osnove metoda mnogourovnevoj asimptoticheskoj gomogenizacii i konechno-elementnogo resheniya trekhmernyh zadach teorii uprugosti [MultiScale_SMCM program for multiscale modeling of the stress-strain state of structures made of composite materials, based on the method of multilevel asymptotic homogenization and finite element solution of three-dimensional problems of elasticity theory]: certificate of ofic. registration of computer programs/ Yu.I. Dimitrienko, S.V. Sborshchikov, Yu.V. Yurin; applicant and copyright holder: BMSTU — no. 2018677684; application 21.02.2018; registered in the register of computer programs 17.04.2018 — [1].
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